A special Lagrangian fibration of smooth compact Calabi-Yau 3-fold. (progress report)

Alexei Kovalev
Cambridge University

We construct a compact smooth Ricci-flat K\"ahler 3-fold as
a carefully chosen `generalized connected sum' of two asymptotically
cylindrical manifolds taken at their cylindrical ends. A special
Lagrangian (SL) fibration is obtained on each of the two non-compact
pieces with typical fibre a 3-torus (and some singular fibres). By
proving a gluing theorem for these fibrations a SL fibration is
obtained on the connected sum.

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